Question 1
Taxicab Example of Bayesian Thinking
• Suppose there has been a hit-and-run accident. A person was struck by a taxicab last night. There
are two cab companies in town, Blue Cab and Green Cab. The only witne
...
Question 1
Taxicab Example of Bayesian Thinking
• Suppose there has been a hit-and-run accident. A person was struck by a taxicab last night. There
are two cab companies in town, Blue Cab and Green Cab. The only witness, who was some distance
away, believes it was a blue vehicle he saw cause the accident. Which cab company is guilty?
• Green Cab Company had 90 cabs on the street at the time of the accident, while Blue Cab Company
had only 10 cabs out.
• Given the lighting and visibility at the time of the accident, a person could correctly distinguish a blue
from a green cab about 80% of the time, at the distance the witness said he was from the accident.
(One can always tell if it was a taxicab or not.)
What is the probability that the cab was from Blue Cab? (Answer: approximately 30%.)
G − green cab
B − blue cab
T − Testimony is Blue cab
P(G) = 0:9; P(B) = 0:1
P(TjB) = 0:8
P(Tj:B) = P(TjG) = 0:2
P(BjT) = P(TjB)P(B)
P(T) =
P(TjB)P(B)
P(TjB)P(B) + P(Tj:B)P(:B) =
0:8 · 0:1
0:8 · 0:1 + 0:2 · (1 − 0:1) ≈ 0:308
Question 2
Question 1
We believe that the relation between the Boolean variables A, B, C can be approximated by: A ! B and
B ! C. A careful examination of the conditional probabilities gives:
Prob(A) = 0:2; Prob(B j A = 0) = 0:7; Prob(B j A = 1) = 0:8
Prob(C j B = 0) = 0:5; Prob(C j B = 1) = 0:6
Produce a graphic representation of this as a Bayesian network
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